My favorite time is in the fall, late September/Early October. However, this is the heart of hurricane season, so there is a chance that you'll get re-routed. This is part of the adventure for me.
I like this season because the ships tend to be less crowded and the weather (and water) is still nice and warm (hot even) in the Caribbean. Also, it's not quite the high season in the Caribbean, and the ports tend to be less crowded. For example, on my last two cruises, one in September and one in December, there were three ships in port at St. Thomas in September, and five for the December trip. That's 4000 or so extra people invading the port on the same day we were.